Is there any theorem from linear algebra about writing random variables as a linear combination...

letumsnemesislh

letumsnemesislh

Answered

2022-07-03

Is there any theorem from linear algebra about writing random variables as a linear combination of their elements?
Suppose that X is a random variable which belongs to a standard probability space ( Ω , B , μ ). Could anybody provide some theorem and its details where X can be written as X = i = 1 k w i x i , where w i 0 and x i R ?

Answer & Explanation

billyfcash5n

billyfcash5n

Expert

2022-07-04Added 17 answers

Solution:
Sure, not a fancy theorem, but suppose X is a real-valued random variable with finite support { x 1 , . . . , x k }. Then X = i = 1 k 1 X = x i x i ..
Notice the indicator weights are Bernoulli random variables.

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